GCF of 329/42, 705/5722
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 329/42, 705/5722 i.e 47/120162 easily. The following is the detailed procedure to determine the greatest common factor of fractions 329/42, 705/5722.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 329/42,705/5722?
Given fractions are 329/42,705/5722
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 329/42,705/5722, numerators are 329,705
Denominators are 42,5722
The GCF of 329,705 is 47 .
LCM of 42,5722 is 120162.
The greatest common factor of 329/42,705/5722 = [GCF of 329,705]/[LCM of 42,5722]= 47/120162
Therefore, the GCF of 329/42,705/5722 is 47/120162.
To find the highest common factor of 329,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 329 are 1, 7, 47, 329
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 329,705 is 47.
Lets's calculate GCF of 329,705
| 47 | 329, 705 |
| 7, 15 |
∴ So the GCF of the given numbers is 47 = 47
Greatest Common Factor of 329,705 By Matching Biggest Common Factor Method
Now, list down the factors of 329
:1,7,47,329
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 329,705 . The biggest common factor number is the GCF number.
So the greatest common factor 329,705 is 47.
Lets's calculate LCM of 42,5722
| 2 | 42, 5722 |
| 21, 2861 |
∴ So the LCM of the given numbers is 2 x 21 x 2861 = 120162
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 47/120162
Therefore, the GCF of Fractions 329/42,705/5722 is 47/120162
Least Common Multiple of 42,5722 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 42,5722 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,5722) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(42,5722) x common factors =2 x 1 = 2
LCM(42,5722) = ( 42 × 5722 ) / 2
LCM(42,5722) = 240324 / 2
LCM(42,5722) = 120162
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FAQs on GCF of Fractions of 329/42, 705/5722
1. What is the HCF of 329,705?
The HCF of 329,705 is 47
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 329/42, 705/5722?
Answer: GCF of Numerators as per given numbers 329/42, 705/5722 is
GCF of Numerators i.e. for 329,705 is 47
LCM of denominators i.e. for 42,5722 is 120162.
Thus, GCF of Fractions is 47/120162.Finally, GCF of Fractions for 329/42, 705/5722 is 47/120162.